I would go with whatever makes the encounter more fun for the players. If things are going badly for them, maybe give them a break for a round and have one of the NPCs stop to reload. Or just go by the same rules as the players and follow the auto fire and multiple quick shot rules.

The rules as written are correct. What the rules are saying, is that there are only a few situations where NPCs/PCs runs out of ammo. For PCs, they can also run out of ammo when the Gamemaster uses DP.

So if an PC/NPC uses automatic fire or does 3 quick shots in one round, they run out of ammo. The difference is, NPCs always have however many reloads they need (i.e. the GM has free license with NPCs). If it makes a good story moment for them to be out of ammo (maybe so they have to surrender and give the PCs vital info), then they run out. If they should keep fighting, then they have one more reload. If you want the PCs to be able to collect extra ammo off the NPC corpses, then they can be carrying extra reloads. If you don't want your PCs to get extra weapons, then the NPCs' gun is empty at the end of the fight.

The rules as written are correct. What the rules are saying, is that there are only a few situations where NPCs/PCs runs out of ammo. For PCs, they can also run out of ammo when the Gamemaster uses DP.

So if an PC/NPC uses automatic fire or does 3 quick shots in one round, they run out of ammo. The difference is, NPCs always have however many reloads they need (i.e. the GM has free license with NPCs). If it makes a good story moment for them to be out of ammo (maybe so they have to surrender and give the PCs vital info), then they run out. If they should keep fighting, then they have one more reload. If you want the PCs to be able to collect extra ammo off the NPC corpses, then they can be carrying extra reloads. If you don't want your PCs to get extra weapons, then the NPCs' gun is empty at the end of the fight.

Sorry but this does not address the question asked.
Does a NPC that has just fired on auto
a) keep shooting (because you follow the "Don't keep track of resources or gear for the NPCs" rule)?
or
b) stop shooting (because you follow the "Normally, NPCs cannot reload their weapons" rule)?

Saying "the rules as written are correct" is not helpful, since it implies there is no issue. But there IS an issue. The issue is that the rule NPCs need to spend DPs to reload makes no sense if the other rule means they have free reloads.

Let me ask you this: could it be that you are confusing reload the action with reload the equipment?

We can arrive at a consistent state if we read the two rules as follows:

"Don't keep track of resources or gear for the NPCs" = whenever the NPC attempts Reload the action, they always have a Reload the equipment handy. They never fail the action because they have run out of equipment.

"Normally, NPCs cannot reload their weapons." = when the rules indicate a NPC needs to take the Reload action, it instead switches to another weapon or tactic. Only if the DM spends a DP will the NPC take the reload action. Why? It doesn't matter why.

The implication and answer is then:

NPCs that need to reload generally find themselves out of ammo. Unless the DM spends a DP, in which case they did have extra ammo after all.

Like with PCs, NPCs only run out of ammo when the rules indicate a reload.

Feel free to interpret a reload as the gun jamming; anything that explains why the NPC abandons the weapon to try something else.

Sorry but this does not address the question asked.
Does a NPC that has just fired on auto
a) keep shooting (because you follow the "Don't keep track of resources or gear for the NPCs" rule)?
or
b) stop shooting (because you follow the "Normally, NPCs cannot reload their weapons" rule)?

Saying "the rules as written are correct" is not helpful, since it implies there is no issue. But there IS an issue. The issue is that the rule NPCs need to spend DPs to reload makes no sense if the other rule means they have free reloads.

Let me ask you this: could it be that you are confusing reload the action with reload the equipment?

There could be some confusion between action and equipment. How about this:
NPCs and PCs follow the same rules. If an NPC uses the slow action "automatic fire" and they keep rolling until they get a 1, then they're out of ammo. They cannot take the reload action (and thus that weapon will be empty for the combat) unless they a) take the reload action (a normal action), which requires the GM to spend a darkness point, and b) they have the "reload" equipment item of the appropriate technology level (primitive, ordinary, or advanced).

Zapp:

The implication and answer is then:

NPCs that need to reload generally find themselves out of ammo. Unless the DM spends a DP, in which case they did have extra ammo after all.

Like with PCs, NPCs only run out of ammo when the rules indicate a reload.

Feel free to interpret a reload as the gun jamming; anything that explains why the NPC abandons the weapon to try something else.